On closed characteristics of minimal action on a convex three-sphere

The uploaded paper proves exactly the statement invoked by the model: on the boundary of any uniformly convex domain in R^4, every action-minimizing closed characteristic (systole) bounds a disk-like global surface of section (Theorem 1) . The paper’s introduction provides a proof sketch that matches the model’s outline: construct a uniformly convex Hamiltonian with a constant orbit and a split pair of orbits near the systole; use the Abbondandolo–Kang isomorphism to relate the Morse complex of Clarke’s dual functional to the Floer complex (Theorem 5.3), deducing a nontrivial Floer count; apply neck-stretching to obtain a degree-1 evaluation map on a moduli space of finite-energy J-holomorphic planes; and conclude embedded disk-like pages and a global surface of section, then remove nondegeneracy/uniqueness via perturbation (the sketch and the technical steps appear in the Introduction and Sections 5–8) . The model’s solution is essentially a concise restatement of the paper’s own approach. Minor omissions (e.g., the upgrade to integer coefficients and the explicit perturbation scheme on S^3) do not affect correctness.